To begin with, a conventional antenna device using a Rotman lens will be explained with its top plan view in FIG. 8. In FIG. 8, the reference numeral (1) denotes a Rotman lens. The reference numerals (21),(22), - - - (2m) denote respective ones of a plurality of input ports for feeding electric power, and the reference numerals (31),(32), - - - (3n) denote respective ones of a plurality of output ports for extracting electric power in the Rotman lens (1). The reference numerals (41),(42), - - - (4n) denote respective ones of a plurality of antenna elements for radiating electromagnetic waves to space, and the reference numeral (5) denotes an array antenna having the plurality of antenna elements (41),(42), - - - (4n) arranged linearly. The reference numerals (61),(62), - - - (6n) denote respective ones of a plurality of transmission lines connecting respective ones of the output ports to respective ones of the antenna elements, and the reference numeral (7) denotes a line section comprised of the transmission lines (61),(62), - - - (6n) having different lengths. The reference numeral (8) denotes a center line. This antenna device is line-symmetric with respect to the center line (8). The reference numeral (9) denotes an auxiliary line for indicating a position of one (21) of the input ports. The input port (21) is located in a direction at an elevation angle α with respect to the center line (8) when viewed from S2 which is an origin of an X-Y coordinate system. The reference numeral (10) denotes a straight line which is indicative of a spatial beam direction upon excitation of the input port (21), and oriented in a direction at an angle β with respect to a direction facing a front of the array antenna. In a primitive or basic design process, a Rotman lens is generally designed under a condition of β=α.
In the conventional antenna device configured as above, when one of the input ports (21),(22), - - - (2m) is excited, electric power is fed into the Rotman lens (1). The electric power in the Rotman lens (1) is extracted from each of the output ports (31),(32), - - - (3n), and transmitted to a corresponding one of the antenna elements (41),(42), - - - (4n) through a respective one of the transmission lines (61),(62), - - - (6n). An excitation amplitude and an excitation phase of the array antenna (5) are determined by which of the input ports (21),(22), - - - (2m) is excited, and the spatial beam direction is determined by the excitation phase of the array antenna (5).
In the conventional antenna device illustrated in FIG. 8, the input ports (21),(22), - - - (2m) are arranged on an arc having a radius R from a center located at a focal point S1 of the Rotman lens. The origin S2 of the X-Y coordinate system is represented by an intersecting point of the center line (8) with a curve segment having the output ports (31), (32), - - - , (3n) arranged thereon. S3 indicates an intersecting point of the center line (8) with a curve segment having the input ports (21), (22), - - - , (2m) arranged thereon. An x coordinate and a y coordinate of each of the output ports (31),(32), - - - (3n), and an electrical length w of each of the transmission lines (61),(62), - - - (6n), are expressed in the following Formulas 1 to 3, respectively:x=[2w(1−g)−b02η2]/2(g−a0)  (1)y=η(1−w)  (2)w=[−b−√{square root over ((b2−4ac))}]/2a  (3)
In the above Formulas 1 to 3,g=G/F,η=Ln/F,a0=cos α,b0=sin α,a=1−η2−[(g−1)/(g−a0)]2,b=2g(g−1)/(g−a0)−[(g−1)/(g−a0)2]b02η2+2η2−2g, andc=gb02η2/(g−a0)−b04η4/[4(g−a0)2]−η2.
Further, the radius R is expressed in the following formula:R=[(Fa0−G)2+F2+b02]/[2(G−Fa0)]  (4)
In the Formula 4, G is a size of the Rotman lens defined by a distance between S2 and S3. Further, F is a distance between the input port (21) and S2, and 2 Ln is an aperture length of the array antenna (5). In the basic design process, it is commonly considered that it is desirable to set approximately in the following range: 0.8<η<1, i.e., set F in a range of about 1 to 1.25 times Ln, and set g to about 1.137, under a defined condition of β=α, in view of an advantage of being able to reduce an error in excitation phase at each of the output ports (31), (32), - - - (3n).